TY - JOUR
T1 - Sobolev extension by linear operators
AU - Fefferman, Charles L.
AU - Israel, Arie
AU - Luli, Garving K.
PY - 2013
Y1 - 2013
N2 - Let Lm,pℝn) be the Sobolev space of functions with mth derivatives lying in Lp(ℝn). Assume that n< p < ∞. For E ⊂ ℝn, let Lm,p(E) denote the space of restrictions to E of functions in Lm,pℝn). We show that there exists a bounded linear map T: Lm,p(E) → Lm,pℝn) such that, for any f ∈ Lm,p(E), we have Tf = f on E. We also give a formula for the order of magnitude of {norm of matrix}f{norm of matrix}Lm,p(E) for a given f: E → ℝ when E is finite.
AB - Let Lm,pℝn) be the Sobolev space of functions with mth derivatives lying in Lp(ℝn). Assume that n< p < ∞. For E ⊂ ℝn, let Lm,p(E) denote the space of restrictions to E of functions in Lm,pℝn). We show that there exists a bounded linear map T: Lm,p(E) → Lm,pℝn) such that, for any f ∈ Lm,p(E), we have Tf = f on E. We also give a formula for the order of magnitude of {norm of matrix}f{norm of matrix}Lm,p(E) for a given f: E → ℝ when E is finite.
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U2 - 10.1090/S0894-0347-2013-00763-8
DO - 10.1090/S0894-0347-2013-00763-8
M3 - Article
AN - SCOPUS:84883362530
SN - 0894-0347
VL - 27
SP - 69
EP - 145
JO - Journal of the American Mathematical Society
JF - Journal of the American Mathematical Society
IS - 1
ER -